Transmitting and receiving systems that receive transmission data transmitted from a transmitter with a receiver have been known. In such a transmitting and receiving system, the transmitter and the receiver are associated with each other. The receiver recognizes only the transmission data transmitted from the associated transmitter as the transmission data that is intended to be transmitted to the receiver itself. The transmitter includes a transmitter memory, which stores individual identification information, and a power source. The receiver includes a receiver memory, which stores the identification information of the associated transmitter. With this configuration, the same identification information is registered in the receiver and the transmitter associated with the receiver. Since the same identification information is registered, the transmitter and the receiver are associated with each other. The transmitter generates transmission data containing data indicating information intended to be received by the receiver and verification data for allowing the receiver to verify the identification information. The transmitter then transmits the generated transmission data to the receiver. Upon reception of the transmission data, the receiver verifies the identification information of the transmitter that has transmitted the transmission data against the identification information registered in the receiver based on the verification data contained in the transmission data and the identification information stored in the receiver memory. If the identification information registered in the transmitter that has transmitted the transmission data matches the identification information registered in the receiver, the receiver recognizes that the transmission data is the transmission data that is intended to be transmitted to the receiver itself.
One example of the transmitting and receiving system includes, for example, a transmitting and receiving system disclosed in Patent Document 1. The transmitter disclosed in Patent Document 1 computes exclusive OR data by taking the exclusive OR of fixed data, which is the data indicating the identification information, and variable data that may have different values. The transmitter transmits the transmission data with the computed exclusive OR data serving as the verification data. The receiver restores the fixed data and the variable data from the received transmission data by obtaining the exclusive OR of the fixed data stored in the receiver memory and the exclusive OR data. The receiver verifies the fixed data stored in the receiver memory against the fixed data restored from the exclusive OR data.
The transmission of the transmission data consumes electric power of the power source. It is, therefore, necessary to reduce the electric power required for the transmission of data to extend the life of the power source. For this reason, it is desired to reduce the data length of the transmission data transmitted from the transmitter. The transmitter disclosed in Patent Document 1 transmits the transmission data containing the exclusive OR data instead of the fixed data and the variable data. Thus, the data length of the transmission data is shorter than a case in which the fixed data and the variable data are transmitted. However, in the case of taking the exclusive OR of the fixed data and the variable data, the data length of the fixed data is equal to the data length of the exclusive OR data. That is, the data length of the exclusive OR data does not become shorter than that of the fixed data. Thus, in the transmitter disclosed in Patent Document 1, the fixed data hinders reducing the data length of the transmission data.